1、 1 2 1 2 3 4 1.(2016 ) ,AB O ,AC , BAC AD O D,DE AC AC E,OE AD F. (1) :DE O ; (2) =, . (1) : OD, OA=OD, ODA= OAD, BAC AD, OAD= DAC, DAC= ODA, OD AE. DE AE, DE OD, OD O , DE O . (2) : BC,DB, D DH AB H, AB O , ACB=90 , Rt ABC ,cos CAB= =. OD AE, DOH= CAB, 2 cos DOH=cos CAB=. Rt HOD ,cos DOH= , =, OD=5
2、x, AB=10x,OH=3x, Rt HOD ,DH= =4x, AH=AO+OH=8x, Rt HAD ,AD 2 =AH 2 +DH 2 =80x 2 , BAD= DAE, AED= ADB=90 . ADE ABD, = , AD 2 =AE AB=AE 10x, AD 2 =80x 2 , AE=8x, OD AE, AEF DOF, = =. 2.(2016 ) , ABCD O, AB O , D O BA M. (1) MD=6,MB=12, AB ; (2) AM=AD, DCB . :(1) MD O , MD 2 =MA MB, MD=6, MB=12,MB=MA+AB
3、, MA=3,AB=12-3=9. (2) AM=AD, AMD= ADM, DB, MD O , 3 ADM= ABD, AB O , ADB , BAD=90 - ABD. BAD= AMD+ ADM=2 ABD, 90 - ABD=2 ABD, ABD=30 , BAD=60 . ABCD , BAD+ DCB=180 , DCB=120 . 3. ,AB O , CD AB , AB E, F CD E , BF,AF O M,N. (1) :B,E,F,N ; (2) :AC 2 +BF BM=AB 2 . :(1) BN, AN BN, CD AB, BEF= BNF=90 , B
4、EF+ BNF=180 , B,E,F,N . (2) AC 2 =AE AB, Rt BEF Rt BMA = , BF BM=BA BE=BA (BA-EA), BF BM=AB 2 -AB AE, BF BM=AB 2 -AC 2 , AC 2 +BF BM=AB 2 . 4.(2015 ) ,O ABC , O ABC BC M,N , AD G, AB,AC E,F . 4 (1) :EF BC; (2) AG O , AE=MN=2 , EBCF . (1) : ABC ,AD BC, AD CAB . O AB,AC E,F, AE=AF, AD EF. EF BC. (2) : (1) AE=AF,AD EF, AD EF . EF O , O AD . OE,OM, OE AE. AG O AO=2OE, OAE=30 . ABC AEF . AE=2 , AO=4,OE=2. OM=OE=2,DM=MN= , OD=1. AD=5,AB= . EBCF ( ) 2 - (2 ) 2 = .
